Simplify the following expression: $ k = \dfrac{q + 9}{q - 8} - \dfrac{-5}{7} $
Answer: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{q + 9}{q - 8} \times \dfrac{7}{7} = \dfrac{7q + 63}{7q - 56} $ Multiply the second expression by $\dfrac{q - 8}{q - 8}$ $ \dfrac{-5}{7} \times \dfrac{q - 8}{q - 8} = \dfrac{-5q + 40}{7q - 56} $ Therefore $ k = \dfrac{7q + 63}{7q - 56} - \dfrac{-5q + 40}{7q - 56} $ Now the expressions have the same denominator we can simply subtract the numerators: $k = \dfrac{7q + 63 - (-5q + 40) }{7q - 56} $ Distribute the negative sign: $k = \dfrac{7q + 63 + 5q - 40}{7q - 56}$ $k = \dfrac{12q + 23}{7q - 56}$